We don't know that's how the binder works. It's most likely it doesn't work like that. There's a binder for channelers and a binder for non-channelers and personally I think it has to do with physical differences, namely that channelers have different brains, or at least, their minds become altered when they're teenagers and exposed to the Source for the first time.

You don't even need to hold the Source to be bound... someone else can channel Spirit into the rod, so long as you touch it. A link would be just as useless, and even worse, the Sisters around would definitely notice. Mesaana would never trust her fate to the treacherous Black Ajah anyway... Liandrin was a murderous sneak at the best of times around Moghedien.